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3 years ago

If you have 100 feet of fence, which measurements would give you the largest area?

Mathematics

1 answer:

ivolga24 [154]3 years ago

3 0

Answer:

25x25x25x25 Perfect square!

Step-by-step explanation:

Perfect square will always give you the most surface area.

So in this case...

100/4=25ft each side.

Thanks for letting me help!!

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What will be the value of

madreJ [45]

The expression as given doesn't make much sense. I think you're trying to describe an infinitely nested radical. We can express this recursively by

$\begin{cases}a_1=\sqrt{42}\\a_n=\sqrt{42+a_{n-1}}\end{cases}$

Then you want to know the value of

$\displaystyle\lim_{n\to\infty}a_n$

if it exists.

To show the limit exists and that $a_n$ converges to some limit, we can try showing that the sequence is bounded and monotonic.

Boundedness: It's true that $a_1=\sqrt{42}\le\sqrt{49}=7$ . Suppose $a_k\le 7$ . Then $a_{k+1}=\sqrt{42+a_k}\le\sqrt{42+7}=7$ . So by induction, $a_n$ is bounded above by 7 for all $n$ .

Monontonicity: We have $a_1=\sqrt{42}$ and $a_2=\sqrt{42+\sqrt{42}}$ . It should be quite clear that $a_2>a_1$ . Suppose $a_k>a_{k-1}$ . Then $a_{k+1}=\sqrt{42+a_k}>\sqrt{42+a_{k-1}}=a_k$ . So by induction, $a_n$ is monotonically increasing.

Then because $a_n$ is bounded above and strictly increasing, the limit exists. Call it $L$ . Now,

$\displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty}a_{n-1}=L$

$\displaystyle\lim_{n\to\infty}a_n=\lim_{n\to\infty}\sqrt{42+a_{n-1}}=\sqrt{42+\lim_{n\to\infty}a_{n-1}}$

$\implies L=\sqrt{42+L}$

Solve for $L$ :

$L^2=42+L\implies L^2-L-42=(L-7)(L+6)=0\implies L=7$

We omit $L=-6$ because our analysis above showed that $L$ must be positive.

So the value of the infinitely nested radical is 7.

4 0

3 years ago

I am having a hard time with simultaneous equations specifically the elimination method, i want to know when do we subtract and

ElenaW [278]

Answer:

The solution to these two equations is (3, 1)

Step-by-step explanation:

So for the elimination method, we are basically multiply each equation by a factor that would allow us to cancel them out..

We could rewrite the equations as the following to make the elimination method easier:

-2y + 3x = 7

y + 4x = 13

We could multiply the second equation by positive 2 in order to cancel out the y from the first equation when we add.

-2y + 3x = 7

2y + 8x = 26 ---> Now we have 11x = 33, when we simplify, we have x = 3.

Now to find our y value in order to find the solution, we would just plug in our x value and solve for y. **We can use either equation to find the answer for this...

-2y + 3x =7.

-2y + 3(3) = 7

-2y + 9 = 7

-2y = -2

y = 1.

We can double check our answer by plugging in both x and y values into the second equation.

4(3) + 1 = 13.

12 + 1 = 13, so we are correct.

The solution to these two equations is (3, 1)

6 0

3 years ago

Please help me with this question....

hichkok12 [17]

Answer:

Person D

Step-by-step explanation: Because when you subtract the deductions from what the people earned. Person D has the least amount of money.

7 0

3 years ago

The function h(t) = 200 – 17t represents the height of a ball (in feet) dropped from 400 feet after t seconds. What will the hei

GenaCL600 [577]

Answer:

160.9 feet

Step-by-step explanation:

The function h(t) = 200 – 17t represents the height of a ball (in feet) dropped from 400 feet after t seconds.

After 2.3 seconds,

h(t) = 200 – 17t

h(2.3) = 200 – (17 X 2.3)

= 200 - 39.1

=160.9 feet

After 2.3 seconds, the ball drops to a height of 160.9 feet.

5 0

4 years ago

List the square numbers less than 90 and greater than 50

Setler79 [48]

$7^2=49 \ \textless \ 50-NOT\\8^2=64-YES\\9^2=81-YES\\10^2=100 \ \textgreater \ 90-NOT$

5 0

4 years ago